Ok, now that you've pointed it out, I'm not so sure I can find the part about the palm of God's hand.
As for Here I am Lord, I really see it as a great song, and an inspiration. As for holding God's people in one's heart, it means to love all and serve all. As Jesus loved and served and demonstrated at the Last Supper. Its also always spoke to me about St. Peter and the apostles who fostered the early Church by holding all the early Christians in their heart. Its a song that makes one seriously reflect on a possible vocation, at least it does to me.
Some of the other songs can get too inclusive language'y and its about feelings(ugh I hate it when it goes to feelings). But I was looking for why these songs are liturgically wrong. I know no better for songs, so I was hoping you'ld help me see it.
Looks some others like american colleen have touched on that.
For me they aren't so much wrong as less than they could be. The music bothers me more than the lyric content in most of the hymns. Although, when I sing (and I do sing even if I am groaning inside) "I will hold Your people...", I can't help but think, "Hey, it's all about ME, babe." Not a well oriented thought and not our actual experience.
As for "palm of His hand", I think I would be able to find that in one of the Psalms. Maybe the rest of the refrain could be located somewhere but it all seems cobbled together.
And I detest it when the responsorial Psalm is sung in a 'modern' translation. We're not idiots, we can understand a fairly straight translation of the ancient phrases of the Psalms. It seems very condescending to dumb down the phrasing.